Apparatus and method for calibrating analog phased antenna array

ABSTRACT

A method and an apparatus are provided. The method includes (a) turning on an antenna of an antenna array, wherein other antennas of the antenna array are turned off; (b) measuring power for the antenna at each phase of a phase array; (c) repeating step (b) for each antenna of the antenna array; and (d) estimating gain errors based on the measured power for each antenna of the antenna array at each phase of the phase array.

PRIORITY

This application claims priority under 35 U.S.C. § 119(e) to a U.S.Provisional Patent Application filed on Apr. 18, 2019 in the UnitedStates Patent and Trademark Office and assigned Ser. No. 62/835,595, theentire contents of which are incorporated herein by reference.

FIELD

The present disclosure relates generally to wireless communicationsystems, and more particularly, to an apparatus and method forcalibrating an analog phased antenna array.

BACKGROUND

In an antenna array system, an overall radiation pattern may be steeredin an intended direction by applying a certain set of phases on eachantenna, based on knowledge of a geometry of the antenna array. The setof phases for all antennas for a particular steering direction may bereferred to as a codeword and a set of codewords for several directionsmay be referred to as a phase array codebook. While a phase arraycodebook may be designed for an ideal array, there may be an additionalunknown phase error and gain error associated with each antenna due tolayout and circuit imperfections. Such errors may cause a radiationpattern of an antenna array to be different from an intended radiationpattern for each codeword, thereby affecting the overall coverage.Therefore, antennas may be calibrated to have a correct beam pattern percodeword, which essentially refers to learning the gain and phaseerrors. Typically, such errors are independent of the applied phases(i.e., codewords). Typical methods for calibrating antennas focus onscenarios in which errors are dependent only on the antenna and not onthe phase applied. For example, a rotating-element electric field vectormethod and a phase toggle method provide calibration of antennas whenerrors are independent of phase applied. However, in analog beamforming,the errors may be dependent on the phases applied on the antennas.

SUMMARY

According to one embodiment, a method is provided. The method includes(a) turning on an antenna of an antenna array, wherein other antennas ofthe antenna array are turned off; (b) measuring power for the antenna ateach phase of a phase array; (c) repeating step (b) for each antenna ofthe antenna array; and (d) estimating gain errors based on the measuredpower for each antenna of the antenna array at each phase of the phasearray.

According to one embodiment, an apparatus is provided. The apparatusincludes a controller configured to a power meter; and a controllerconfigured to (a) turn on an antenna of the antenna array, wherein otherantennas of the antenna array are turned off; (b) control the powermeter to measure power for the antenna at each phase of a phase array;(c) repeat step (b) for each antenna of the antenna array; and (d)estimate gain errors based on the measured power for each antenna of theantenna array at each phase of the phase array.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other aspects, features, and advantages of certainembodiments of the present disclosure will be more apparent from thefollowing detailed description, taken in conjunction with theaccompanying drawings, in which:

FIG. 1 illustrates an exemplary block diagram of an error model of anantenna array, according to an embodiment;

FIG. 2 illustrates an exemplary block diagram of an apparatus forcalibrating an analog phased antenna array, according to an embodiment;

FIG. 3 illustrates an exemplary flowchart of a method of calibrating ananalog phased antenna array, according to one embodiment;

FIG. 4 illustrates an exemplary diagram of antennas and phases with onereference measurement, according to one embodiment;

FIG. 5 illustrates an exemplary diagram of antennas and phases with tworeference phase measurements, according to one embodiment;

FIG. 6 illustrates an exemplary diagram of antennas and phases, where asecond estimated reference phase is selected, according to oneembodiment;

FIG. 7 illustrates an exemplary diagram of antennas and phases, where asign of an estimated reference phase is resolved, according to oneembodiment;

FIG. 8 illustrates an exemplary diagram of antennas and phases, wherephases of multiple antennas are measured with reference to estimatedreference phases, according to one embodiment;

FIG. 9 illustrates an exemplary diagram of antennas and phases, wherephases of an antenna are measured with reference to estimated referencephases, according to one embodiment;

FIG. 10 illustrates an exemplary diagram of antennas and phases, wherephases of an antenna are measured with reference to two estimatedphases, according to one embodiment;

FIG. 11 is an illustration of selecting candidate codewords for acertain direction, according to one embodiment; and

FIG. 12 is a flowchart of a method of obtaining updated codewords afteranalog phased antenna array calibration, according to one embodiment.

DETAILED DESCRIPTION

Hereinafter, embodiments of the present disclosure are described indetail with reference to the accompanying drawings. It should be notedthat the same elements will be designated by the same reference numeralsalthough they are shown in different drawings. In the followingdescription, specific details such as detailed configurations andcomponents are merely provided to assist with the overall understandingof the embodiments of the present disclosure. Therefore, it should beapparent to those skilled in the art that various changes andmodifications of the embodiments described herein may be made withoutdeparting from the scope of the present disclosure. In addition,descriptions of well-known functions and constructions are omitted forclarity and conciseness. The terms described below are terms defined inconsideration of the functions in the present disclosure, and may bedifferent according to users, intentions of the users, or customs.Therefore, the definitions of the terms should be determined based onthe contents throughout this specification.

The present disclosure may have various modifications and variousembodiments, among which embodiments are described below in detail withreference to the accompanying drawings. However, the present disclosureis not limited to the described embodiments, but includes allmodifications, equivalents, and alternatives within the scope of thepresent disclosure.

Although the terms including an ordinal number such as first, second,etc., may be used for describing various elements, the structuralelements are not restricted by the terms. The terms are only used todistinguish one element from another element. For example, withoutdeparting from the scope of the present disclosure, a first structuralelement may be referred to as a second structural element. Similarly,the second structural element may also be referred to as the firststructural element. As used herein, the term “and/or” includes any andall combinations of one or more associated items.

The terms used herein are merely used to describe various embodiments ofthe present disclosure but are not intended to limit the presentdisclosure. Singular forms are intended to include plural forms unlessthe context clearly indicates otherwise. In the present disclosure, theterms “include” or “have” indicate existence of a feature, a number, astep, an operation, a structural element, parts, or a combinationthereof, and do not exclude the existence or probability of the additionof one or more other features, numerals, steps, operations, structuralelements, parts, or combinations thereof.

Unless defined differently, all terms used herein have the same meaningsas those understood by a person skilled in the art to which the presentdisclosure belongs. Terms such as those defined in a generally useddictionary are to be interpreted to have the same meanings as thecontextual meanings in the relevant field of art, but are not to beinterpreted to have ideal or excessively formal meanings unless clearlydefined in the present disclosure.

According to one embodiment, an apparatus and method estimates phasedependent errors on an antenna array by selectively turning on antennasin the antenna array with certain phases on the antennas and measuringpower received only in a boresight direction. The apparatus and methodfurther perform calculations on the power measurements to obtain errorvalues. The error values may be used to adjust or update a phase arraycodebook for application to a phase array that has impairments.

According to one embodiment, an apparatus includes an antenna array withN elements, where N is a positive integer. For example, the antennaarray has greater than two elements. The phase level is quantized with Qbits, where Q is a positive integer, hence the possible phases on theantennas are

$\left\{ {0,\frac{\pi}{2^{Q - 1}},\ldots \mspace{14mu},\ \frac{\left( {2^{Q} - 1} \right)\pi}{2^{Q - 1}}} \right\}.$

For example, the phase level is quantized with one or more bits. Theoutput from the ith antenna is received in the boresight direction as inEquation (1):

√{square root over (P)}α_(i)ρ_(ik) e ^(1j·(ψ) ^(i) ^(θ) ^(k) ^(+σ) ^(ik)⁾   (1)

where P is a power, θ_(k) is a phase applied, and ψ_(i), α_(i), ρ_(ik),and σ_(ik) are error terms. The error terms ψ_(i) and α_(i) depend onlyon the antenna, but the error terms ρ_(ik) and σ_(ik) depend on both theantenna and the phase used. The error terms α_(i) and ρ_(ik) on powerare real and positive.

FIG. 1 illustrates an exemplary block diagram of an error model for anantenna array, according to one embodiment.

Referring to FIG. 1, an antenna array 100 includes a digital-to-analogconverter (DAC) 101, a filter and radio frequency (RF) upconverter 103,a phased array transmitter 105, and n antennas 107 a to 107 n, where nis a positive integer, that correspond to n phase shifters 123 a to 123n in the phased array transmitter 105. It is appreciated that any numberof phase shifters corresponding to antennas may be used withoutdeviating from the scope of the present disclosure.

The DAC 101 includes an input 111 for receiving a digital signal and anoutput 113 for outputting an analog version of the received digitalsignal.

The filter and RF upconverter 103 includes an input connected to theoutput 113 of the DAC 101 and an output 115.

The phased array transmitter 105 includes an input connected to theoutput 115 of the filter and RF upconverter 103 and a number of outputs173 a to 173 n, which are equal to the number of phase shifters 123 a to123 n in the phased array transmitter 105, elements for modeling errorterms α_(o 167) a to α_(i) 167 n, and elements for modeling error termsθ₀ 171 a to ψ_(i) 171 n.

The phased array transmitter 105 includes a splitter 117, a number ofthe phase shifters 123 a to 123 n. The phase shifter 123 a includeselements for modeling phases θ₀ to θ_(k) 127 a, 133 a, . . . 139 a. Thephase shifter 123 n includes elements for modeling phases θ₀ to θ_(k)127 n, 133 n, . . . 139 n. The phase shifter 123 a also includeselements for modeling error terms σ₀₀ to σ_(ik) 129 a, 135 a, . . . 141a. The phase shifter 123 n also includes elements for modeling errorterms σ₀₀ to σ_(ik) 129 n, 135 n, . . . 141 n. The phase shifter 123 aalso includes elements for modeling error term ρ₀₀ to ρ_(ik) 131 a, 137a, . . . 143 a. The phase shifter 123 n also includes elements formodeling error term ρ₀₀ to ρ_(ik) 131 n, 137 n, . . . 143 n. The phaseshifter 123 a includes an output 145 a, and the phase shifter 123 nincludes an output 145 n.

The element for modeling error term α₀ 167 a is connected to the output145 a of the phase shifter 123 a and includes an output 169 a. Theelement for modeling error term α_(i) 167 n is connected to the output145 n of the phase shifter 123 n and includes an output 169 n. Theelement for modeling error term ψ₀ 171 a is connected to the output 169a of the element for modeling error term α₀ 167 a and includes an output173 a. The element for modeling error term ψ_(i) 171 n is connected tothe output 169 n of the element for modeling error term α_(i) 167 n andincludes an output 173 n.

The antenna 107 a is connected to one of the outputs 173 a of the phasedarray transmitter 105 associated with the phase shifter 123 a. Theantenna 107 n is connected to one of the outputs 173 n of the phasedarray transmitter 105 associated with the phase shifter 123 n.

FIG. 2 illustrates an exemplary block diagram of an apparatus 200 forcalibrating an analog phased antenna array, according to one embodiment.

Referring to FIG. 2, the apparatus 200 includes a signal generator 201,a phased array 203, and n antennas 205 a, 205 b, . . . , and 205 n, ameasurement antenna 213, a power meter 215, and a controller 217.

The signal generator 201 includes an output 219 for providing a signal.The phased array 203 includes a first input connected to the output 219of the signal generator 201, a second input for receiving a controlsignal from the controller 217, and n outputs 221 a, 221 b, . . . , and221 n. The n antennas 205 a, 205 b, . . . , and 205 n are connected tothe n outputs 221 a, 221 b, . . . and 221 n of the phased array 203,respectively. Each antenna 205 a, 205 b, . . . , and 205 n may transmita signal. It is appreciated that any number of antennas may be usedwithout deviating from the scope of the present disclosure.

The measurement antenna 213 receives a signal transmitted by any of theplurality of antennas 205 a, 205 b, . . . , and 205 n and includes anoutput 229. The power meter 215 includes an input connected to theoutput 229 of the measurement antenna 213, measures a power of a signalreceived by the measurement antenna 213, and includes an output 231 foroutputting the measured power. The controller 217 includes an inputconnected to the output 231 of the power meter 215 for receiving a powermeasurement of a received signal and includes an output 233 connected tothe second input of the phased array 203 for controlling the phasedarray 203 based on the power measurement.

For explicit calibration, the apparatus measures √{square root over(P)}α_(i)ρ_(ik) and ψ_(i)+σ_(ik) for all i and k, where all i and k areeach positive integers greater than zero. Since θ_(k), which is a phaseapplied on an antenna, is known, ψ_(i)+θ_(k)+σ_(ik) may be measuredinstead of ψ_(i)+σ_(ik), where ψ_(i), σ_(ik) are errors.ψ_(i)+θ_(k)+σ_(ik) may be represented by ϕ_(ik), where ϕ_(ik) refers toa total phase on the antenna after including the errors, and where irefers to an antenna number and k refers to a phase. An estimate ofϕ_(ik) may be indicated with a hat as {circumflex over (ϕ)}_(ik). A gainat antenna number i and at phase k may be defined as g_(ik)=√{squareroot over (P)}α_(i)ρ_(ik), where g_(ik) is measured. An estimate ofg_(ik) is indicated as ĝ_(k). An absolute value of ϕ_(ik) cannot bemeasured using power measurements, since all power measurements remaininvariant under a constant added to ϕ_(ik), hence the relative phaseϕ_(ik)−ϕ₀₀ for all (i, k)≠(0,0) is estimated.

FIG. 3 illustrates an exemplary flowchart of a method of calibrating ananalog phased antenna array, according to one embodiment. For example,the method of FIG. 3 may be performed by the apparatus illustrated inFIG. 2.

Referring to FIG. 3, at 301, the apparatus measures power P_(ik) foreach antenna for all phases, where only one antenna is turned on at atime and gain g_(ik) is estimated. The term P_(ik) represents a powermeasured with an i^(th) antenna turned on with phase k and all otherantennas turned off, which provides an estimate for g_(ik)=√{square rootover (P_(ik))} for all (i, k). That is, gain errors g_(ik) are estimatedfrom power measurements as ĝ_(ik)=√{square root over (P_(ik))}.

The term P_(i) ₁ _(k) ₁ _(,i) ₂ _(k) ₂ is defined as a power measuredwith antennas i₁ and i₂ turned on with phases k₁ and k₂, respectively,with all other antennas turned off. Using power measurements P_(i) ₁_(k) ₁ _(,i) ₂ _(k) ₂ , a difference between phases at two antennas maybe obtained. For example, with antenna number 0 (e.g., Ant0) on withphase ϕ₀, antenna number i (e.g., Anti) on with phase θ_(k) and theother antennas turned off, received power is

P_(ik, 00) = |g_(00)e^(1j.(φ₀₀)) + g_(ik)e^(1j.(φ_(ik)))|² = g₀₀² + g_(ik)² + 2g_(ik)g_(00)  cos   (φ_(ik) − φ_(00)).

Since g_(ik) has already been estimated, this measurement may yield anestimate for

$\cos \mspace{11mu} \left( {\varphi_{ik} - \varphi_{00}} \right)\mspace{14mu} {as}\mspace{14mu} {\frac{P_{{ik},00} - P_{ik} - P_{00}}{2\sqrt{P_{ik}P_{00}}}.}$

Since the present method estimates a relative phase ϕ_(ik)−ϕ₀₀,{circumflex over (ϕ)}₀₀ may be set to 0 to obtain an estimate of ϕ_(ik)(i.e., {circumflex over (ϕ)}_(ik)).

FIG. 4 illustrates an exemplary diagram of antennas and phases with onereference measurement, according to one embodiment. Although thefollowing descriptions are provided with reference to fourantennas(e.g., N=4), and three bits for representing phases (e.g., Q=3,equivalently 2^(Q)=2³=8 phases), the present apparatus and method may beapplied to any number of antennas and phases with N≥3, Q≥2.

From cos(ϕ_(ik)), the phases cannot be determined uniquely. Hence, atleast two measurements with respect to two reference phases are requiredfor uniquely determining the phases.

FIG. 5 illustrates an exemplary diagram of antennas and phases with tworeference phase measurements, according to one embodiment. A firstreference may be referred to as {circumflex over (ϕ)}₀₀ and a secondreference may be selected as {circumflex over (ϕ)}_(1R) ₁ where{circumflex over (ϕ)}_(1R) ₁ is to be determined.

Referring again to FIG. 3, at 302, the present apparatus determines thereference phase {circumflex over (ϕ)}_(1R) ₁ . According to oneembodiment, the present apparatus selects R₁ such that |{circumflex over(ϕ)}_(1R) ₁ | is close to

$\frac{\pi}{2}.$

The present apparatus performs measurements P_(1k,00), obtains

${{\cos \mspace{11mu} \varphi_{1k}^{\prime}} = \frac{P_{{1k},00} - P_{1k} - P_{00}}{2\sqrt{P_{1k}P_{00}}}},$

and selects R₁ as

$R_{1} = \left. {\arg \mspace{11mu} \min\limits_{k}} \middle| {\cos \mspace{11mu} \varphi_{1k}^{\prime}} \middle| . \right.$

FIG. 6 illustrates an exemplary diagram of antennas and phases where asecond reference phase {circumflex over (ϕ)}_(1R) ₁ is selected,according to one embodiment.

To resolve the sign of {circumflex over (ϕ)}_(1R) ₁ , the presentapparatus may check the value of cos( ) measurements on the phase thatis ahead of ϕ′_(1R) ₁ by 2^(Q−2) indices. If ϕ′_(1R) ₁ was close to

$\frac{- \pi}{2},$

then shifting the phase value forward by 2^(Q−2) indices from R₁ willcause the new phase to be close to zero, since the phase quantizationhas separation

$\frac{\pi}{2^{Q - 1}}.$

Thus ϕ′_(1(R) ₁ ₊₂ _(Q−2) _()mod(2) _(Q) ₎ will be close to 0, i.e.,cos(ϕ′_(1(R) ₁ ₊₂ _(Q−2) _()mod(2) _(Q) ₎) will be close to +1. Ifϕ′_(1R) ₁ is close to

$\frac{+ \pi}{2},$

then shifting the phase value forward by 2^(Q−2) indices from R₁ willcause the new phase to be close to π, i.e., ϕ′_(1(R) ₁ ₂ _(Q−2)_()mod(2) _(Q) ₎ will be close to π and cos(ϕ′_(1(R) ₁ ₂ _(Q−2)_()mod(2) _(Q) ₎) will be close to −1. Hence {circumflex over (ϕ)}_(1R)₁ =cos⁻¹(cos ϕ′_(1R) ₁ ) if |cos (ϕ′_(1(R) ₁ ₊₂ _(Q−2) _()mod(2) _(Q)₎)+1|≤|cos(ϕ′_(1(R) ₁ ₊₂ _(Q−2) _()mod(2) _(Q) ₎)−1| and {circumflexover (ϕ)}_(1R) ₁ =−cos⁻¹(cos ϕ′_(1R) ₁ ) if |cos(ϕ′_(1(R) ₁ ₊₂ _(Q−2)_()mod(2) _(Q) ₎)−1|<|cos(ϕ′_(1(R) ₁ ₊₂ _(Q−2) _()mod(2) _(Q) ₎)+1|.

FIG. 7 illustrates an exemplary diagram of antennas and phases where thesign of {circumflex over (ϕ)}_(1R) ₁ is resolved, according to oneembodiment. For Q=3, the sign of {circumflex over (ϕ)}_(1R) ₁ may beresolved by looking at the value of cos(ϕ′_(1(R) ₁ _(+2)mod8)).

Thus, if cos(ϕ′_(1(R) ₁ ₊₂ _(Q−2) _()mod(2) _(Q) ₎) is close to +1, then{circumflex over (ϕ)}_(1R) ₁ may be selected as close to

$\frac{- \pi}{2}.$

If cos(ϕ′_(1(R) ₁ ₊₂ _(Q−2) _()mod(2) _(Q) ₎) is close to −1,{circumflex over (ϕ)}_(1R) ₁ may be selected as close to

$\frac{\pi}{2},$

using the estimate for cos ϕ′_(1R) ₁ .

Referring again to FIG. 3, at 303, the present apparatus measures allphases of Anti i≠0,1 with reference to ϕ₀₀ and ϕ_(1R) ₁ . The powermeasurements P_(ik,00) and P_(ik,1R) ₁ are obtained for i≠0,1. Then, theestimates for cos(ϕ_(ik)), cos(ϕ_(ik)−ϕ_(1R) ₁ ) are obtained as

$\frac{P_{{ik},00} - P_{ik} - P_{00}}{2\sqrt{P_{ik}P_{00}}},\frac{P_{{ik},{1R_{1}}} - P_{ik} - P_{1R_{1}}}{2\sqrt{P_{ik}P_{1R_{1}}}},$

respectively.

FIG. 8 illustrates an exemplary diagram of antennas and phases, wherephases of multiple antennas are measured with reference to ϕ₀₀ andϕ_(1R) ₁ , according to one embodiment.

An estimate for ϕ_(ik) may be obtained as follows in Equations (2), (3),(4), and (5):

$\begin{matrix}{A = \frac{P_{ik00} - P_{ik} - P_{00}}{2\sqrt{P_{ik}P_{00}}}} & (2) \\{B = \frac{P_{{ik},{1R_{1}}} - P_{ik} - P_{1R_{1}}}{2\sqrt{P_{ik}P_{1R_{1}}}}} & (3) \\{\begin{bmatrix}u \\v\end{bmatrix} = {\begin{bmatrix}1 & 0 \\{\cos {\overset{\hat{}}{\varphi}}_{1R_{1}}} & {\sin {\overset{\hat{}}{\varphi}}_{1R_{1}}}\end{bmatrix}^{- 1}\begin{bmatrix}A \\B\end{bmatrix}}} & (4) \\{{\overset{\hat{}}{\varphi}}_{ik} = {{Angle}\mspace{14mu} \left( {u + {1{j \cdot v}}} \right)}} & (5)\end{matrix}$

Referring again to FIG. 3, at 304, the present apparatus determines asecond reference phase {circumflex over (ϕ)}_(2R) ₂ . All of the phaseson Anti, where i≠0,1, have been measured. Only one phase {circumflexover (ϕ)}₀₀=0 is estimated for Ant0. For measuring the rest of thephases for Ant0, at least two references are required. One of thereferences may be set as ϕ_(1R) ₁ . The other reference phase fromantenna number 2 (e.g., Ant2) may be selected as ϕ_(2R) ₂ . Similar tohow ϕ_(1R) ₁ was selected in relation to ϕ₀₀, requiring the tworeferences to be approximately

$\frac{\pi}{2}$

apart, me present apparatus selects ϕ_(2R) ₂ in relation to ϕ_(1R) ₁ .The reference ϕ_(2R) ₂ is chosen from the phases of Ant2 such that|cos(ϕ_(2R) ₂ −ϕ_(1R) ₁ )| is closest to zero. This is performed byusing the estimated values of the phases of Ant2 as in Equation (5a) asfollows:

$\begin{matrix}{R_{2} = {\arg {\min\limits_{k}{{\cos \left( {{\overset{\hat{}}{\varphi}}_{2k} - {\overset{\hat{}}{\varphi}}_{1R_{1}}} \right)}}}}} & \left( {5a} \right)\end{matrix}$

At 305, the present apparatus measures all remaining phases of Ant0 withreference to {circumflex over (ϕ)}_(1R) ₁ , {circumflex over (ϕ)}_(2R) ₂. The phase {circumflex over (ϕ)}₀₀ was initially set as zero forreference, the remaining phases of Ant0 is estimated from powermeasurements P_(0k,1R) ₁ , P_(0k,2R) ₂ as follows in Equations (6), (7),(8), and (9):

$\begin{matrix}{A = \frac{P_{{0{k1}},R_{1}} - P_{0k} - P_{1R_{1}}}{2\sqrt{P_{0k}P_{1R_{1}}}}} & (6) \\{B = \frac{P_{{0k},{2R_{2}}} - P_{0k} - P_{2R_{2}}}{2\sqrt{P_{0k}P_{2R_{2}}}}} & (7) \\{\begin{bmatrix}u \\v\end{bmatrix} = {\begin{bmatrix}{\cos {\overset{\hat{}}{\varphi}}_{1R_{1}}} & {\sin {\overset{\hat{}}{\varphi}}_{1R_{1}}} \\{{\overset{\hat{}}{\varphi}}_{2R_{2}}cos} & {\sin {\overset{\hat{}}{\varphi}}_{2R_{2}}}\end{bmatrix}^{- 1}\begin{bmatrix}A \\B\end{bmatrix}}} & (8) \\{{\overset{\hat{}}{\varphi}}_{0k} = {{Angle}\left( {u + {1{j \cdot v}}} \right)}} & (9)\end{matrix}$

FIG. 9 illustrates an exemplary diagram of antennas and phases, wherephases of Ant0 are measured with reference to {circumflex over (ϕ)}_(1R)₁ and {circumflex over (ϕ)}_(2R) ₂ , according to one embodiment. Theprocess of measuring phases of Ant0 with reference to {circumflex over(ϕ)}_(1R) ₁ and {circumflex over (ϕ)}_(2R) ₂ is similar to thedescription of 303 above.

Referring again to FIG. 3, at 306, the present apparatus determines{circumflex over (ϕ)}_(2R) ₃ . The remaining phases to be measured areof Ant1, and it requires at least two references. The first referencemay be selected as {circumflex over (ϕ)}₀₀ and the second reference maybe selected as {circumflex over (ϕ)}_(2R) ₃ . The present apparatus mayselect the reference phase {circumflex over (ϕ)}_(2R) ₃ approximately

$\frac{\pi}{2}$

away from ϕ₀₀, to ensure that |cos({circumflex over (ϕ)}_(2R) ₃−{circumflex over (ϕ)}₀₀)|=|cos({circumflex over (ϕ)}_(2R) ₃ )| isclosest to zero. The present apparatus determines the reference phase{circumflex over (ϕ)}_(2R) ₃ by using the estimated values of the phasesof Ant2 as follows in Equation (10):

$\begin{matrix}{R_{3} = {\arg {\min\limits_{k}{{\cos \left( {\overset{\hat{}}{\varphi}}_{2k} \right)}}}}} & (10)\end{matrix}$

At 307, the present apparatus measures all remaining phases of Ant1 withreference to {circumflex over (ϕ)}₀₀, {circumflex over (ϕ)}_(2R) ₃ . Theremaining phases of Ant1 are estimated from the measurements P_(1k,00),P_(1k,2R) ₃ . The estimate of the k^(th) phase on Ant1, {circumflex over(ϕ)}_(1k) is obtained from power measurements as follows in Equations(11), (12), (13), and (14):

$\begin{matrix}{A = \frac{P_{{1k},{00}} - P_{1k} - P_{00}}{2\sqrt{P_{1k}P_{00}}}} & (11) \\{B = \frac{P_{{1k},{2R_{3}}} - P_{1k} - P_{2R_{3}}}{2\sqrt{P_{1k}P_{2R_{3}}}}} & (12) \\{\begin{bmatrix}u \\v\end{bmatrix} = {\begin{bmatrix}1 & 0 \\{\cos {\overset{\hat{}}{\varphi}}_{2R_{3}}} & {\sin \; {\overset{\hat{}}{\varphi}}_{2R_{3}}}\end{bmatrix}^{- 1}\begin{bmatrix}A \\B\end{bmatrix}}} & (13) \\{{\overset{\hat{}}{\varphi}}_{1k} = {{Angle}\left( {u + {1{j \cdot y}}} \right)}} & (14)\end{matrix}$

FIG. 10 illustrates an exemplary diagram of antennas and phases, wherephases of Ant1 are measured with reference to {circumflex over (ϕ)}₀₀and {circumflex over (ϕ)}_(2R) ₃ , according to one embodiment.P_(1k,00) has already been measured while {circumflex over (ϕ)}_(1R) ₁was being chosen at 302, thus the current measurements required areP_(1k,2R) ₃ . {circumflex over (ϕ)}_(1k) is obtained from P_(1k,00),P_(1k,2R) ₃ using similar calculations as at 305 in FIG. 3.

Referring again to FIG. 3, at 308, the present apparatus optimizes thevalues of ĝ_(ik) and {circumflex over (ϕ)}_(ik). In one embodiment, thepresent apparatus performs a least squared optimization to minimize anerror in the estimates due to noise in the measurements. The variablesmay be changed to

${{\overset{\hat{}}{g}}_{ik}e^{1{j{({\hat{\varphi}}_{ik})}}}} = {g_{rik}^{\prime} + {1{j \cdot g_{cik}^{\prime}}}}$

for performing an optimization as follows in Equations (15) and (16):

$\begin{matrix}{\mspace{79mu} {\left\{ {g_{Rik}^{*^{\prime}},g_{Cik}^{*^{\prime}}} \right\} = {\underset{\{{g_{Rik}^{\prime},g_{Cik}^{\prime}}\}}{Minimize}{f\left( \left\{ {g_{Rik}^{\prime},g_{Cik}^{\prime}} \right\} \right)}}}} & (15) \\{{f\left( \left\{ {g_{Rik}^{\prime},g_{Cik}^{\prime}} \right\} \right)} = {{\sum\limits_{k = 0}^{2^{Q} - 1}{\sum\limits_{i = 0}^{N - 1}\left( {{{g_{rik}^{\prime} + {1{j \cdot g_{cik}^{\prime}}}}}^{2} - P_{ik}} \right)^{2}}} + {\sum\limits_{k = 0}^{2^{Q} - 1}{\sum\limits_{i = 2}^{N - 1}\left( {\left( {{{g_{rik}^{\prime} + {1{j \cdot g_{cik}^{\prime}}} + g_{r00}^{\prime} + {1\; {j \cdot g_{c\; 00}^{\prime}}}}}^{2} - P_{{ik},00}} \right)^{2} + \left( {{{g_{rik}^{\prime} + g_{cik}^{\prime} + g_{r\; 1\; R_{1}}^{\prime} + {1{j \cdot g_{c\; 1\; R_{1}}^{\prime}}}}}^{2} - P_{{ik},{1\; R_{1}}}} \right)} \right)}} + {\sum\limits_{k = 1}^{2^{Q} - 1}\left( {\left( {{{g_{r\; 0k}^{\prime} + {1\; {j \cdot g_{c\; 0\; k}^{\prime}}} + g_{r\; 1\; R_{1}}^{\prime} + {1\; {j \cdot g_{c\; 1\; R_{1}}^{\prime}}}}}^{2} - P_{{0k},{1\; R_{1}}}} \right)^{2} + \left( {{{g_{r\; 0\; k}^{\prime} + {1\; {j \cdot g_{c\; 0k}^{\prime}}} + g_{r\; 2\; R_{2}}^{\prime} + {1\; {j \cdot g_{c\; 2\; R_{2}}^{\prime}}}}}^{2} - P_{{0\; k},\; {2R_{2}}}} \right)^{2}} \right)} + {\sum\limits_{{k \neq R_{1}},{k = 0}}^{2^{Q} - 1}\left( {\left( {{{g_{r\; 1\; k}^{\prime} + {1\; {j \cdot g_{c\; 1k}^{\prime}}} + g_{r\; 0\; 0}^{\prime} + {1\; {j \cdot g_{{c\; 00}\;}^{\prime}}}}}^{2} - P_{{1\; k},00}} \right)^{2} + \left( {{{g_{r\; 1k}^{\prime} + {1\; {j \cdot g_{c\; 1\; k}^{\prime}}} + g_{r\; 2\; R_{3}}^{\prime} + {1\; {j \cdot g_{c\; 2\; R_{3}}^{\prime}}}}}^{2} - P_{{1\; k},\; {2R_{3}}}} \right)^{2}} \right)}}} & (16)\end{matrix}$

The starting point for the optimization is taken from the solutionobtained from the previous steps. The optimal value is used to obtainnew estimates on g_(ik) and ϕ_(ik) as follows in Equation (17):

$\begin{matrix}{{{\hat{g}}_{ik}^{*}e^{1\; {j{({\hat{\varphi}}_{ik}^{*})}}}} = {g_{rik}^{*^{\prime}} + {1{j \cdot g_{cik}^{*^{\prime}}}}}} & (17)\end{matrix}$

According to one embodiment, the optimization problem at 308 may beperformed with a different metric. For example, the form(|g′_(rik)+1j·g′_(cik)+g′_(r00)+1j·g′_(c00)|²−P_(ik,00))² may bereplaced with ||g′_(rik)+1j·g′_(cik)+g′_(r00)+1j·g′_(c00)|²−P_(ik,00)|,||g′_(rik)+1j·g′_(cik)+g′_(r00)+1j·g′_(c00)|−√{square root over(P_(ik,00))}| or ||g′_(rik)+1j·g′_(cik)+g′_(r00)+1j·g′_(c00)|−√{squareroot over (P_(ik,00))}|². This could be any valid distance metric ingeneral.

According to one embodiment, the reference phase {circumflex over (ϕ)}₀₀is set as zero and three other reference phases {circumflex over(ϕ)}_(1R) ₁ , {circumflex over (ϕ)}_(2R) ₂ , {circumflex over (ϕ)}_(2R)₃ are selected. According to another embodiment, the reference phase isset to be another phase from another antenna to be kept as zero andthree other references are chosen from other different antennas. Forexample, the present apparatus may set {circumflex over (ϕ)}₃₆=0 and thethree other references may be selected as {circumflex over (ϕ)}_(0R) ₁ ,{circumflex over (ϕ)}_(1R) ₂ , {circumflex over (ϕ)}_(1R) ₃ .

After estimating the errors, the present apparatus may use the errors tomodify a codebook according to the estimated phase values. When thecodebook is designed with codewords to maximize power in a given set ofdirections {Φ₁, . . . , Φ_(L)}, the present apparatus may obtain newcodewords that maximize power in the directions {Φ₁, . . . , Φ_(L)}, inthe presence of errors. Shifting the phases on the antennas by adding aconstant to all of the phases, does not affect a beam pattern. The shiftto the ideal codeword may be made so that the required phase on thefirst antenna for the codeword matches the estimated value {circumflexover (ϕ)}_(0k) ₀ for some k₀.

For example, the present apparatus obtains candidate codes aftershifting the ideal codeword. Considering an initial (e.g., ideal)codeword [ϕ_(0k) ₀ , ϕ_(1k) ₁ , ϕ_(2k) ₂ , ϕ_(3k) ₃ ] for someparticular steering direction, the present apparatus may shift thecodeword to match {circumflex over (ϕ)}₀₃ in the first position ofcodeword, where the shifted codeword is then [{circumflex over (ϕ)}₀₃,ϕ_(1k) ₁ +{circumflex over (ϕ)}₀₃−ϕ_(0k) ₀ , ϕ_(2k) ₂ +{circumflex over(ϕ)}₀₃−ϕ_(0k) ₀ , ϕ_(3k) ₃ +{circumflex over (ϕ)}₀₃−ϕ_(0k) ₀ ]. For theother antennas, the phases may not be matched exactly with estimatedphase values {circumflex over (ϕ)}_(ik), so there are two closest valuesfor {circumflex over (ϕ)}_(ik) compared to the shifted value ϕ_(ik) _(i)+{circumflex over (ϕ)}₀₃−ϕ_(0k) ₀ . Thus, the total possible codewordsare 2^(Q)*2^(N−1), since there are 2^(Q) possibilities for phases on thefirst antenna and 2 possibilities for phases on each of the remainingN−1 antennas.

FIG. 11 illustrates an exemplary diagram of selecting candidatecodewords for a certain direction, according to one embodiment. In oneembodiment, a steering direction may have a fixed choice for a firstantenna.

Referring to FIG. 11, the present apparatus selects the candidatecodewords for a particular direction for Q=3, N=4. This may be repeatedby going through all phases for the first antenna.

From the candidate codewords for a given steering direction, the presentapparatus may select the codeword that provides the maximum power inthat steering direction. This may be carried out for all steeringdirections.

FIG. 12 illustrates an exemplary diagram of a flowchart of a method forobtaining updated codewords after antenna array calibration, accordingto one embodiment.

Referring to FIG. 12, at 1201, the present apparatus sets a steeringdirection Φ_(d)=Φ₀.

At 1202, the present apparatus obtains ideal code C_(Φ) _(d) =[ϕ_(0k) ₀, ϕ_(1k) ₁ , ϕ_(2k) ₂ , ϕ_(3k) ₃ ] for the steering direction Φ_(d).

At 1203, the present apparatus sets a code phase on the first antenna asC_(0,k) ₀ ={circumflex over (ϕ)}₀₀.

At 1204, the present apparatus obtains 2^(N−1)nearest shifted codewordswith the phase of the first antenna that was set, where N is the numberof antennas, where C_(Φ) _(d) _(,candidates)=[c_(0,k) ₀ , c_(1,k) ₁ ,c_(2,k) ₂ , . . . ], c_(m,k) _(m) ∈ {c_(m1,k) _(m) , c_(m2,k) _(m) }, m∈ [1, N−1], and where c_(m1,k) _(m) and c_(m2,k) _(m) are two anglesclosest to ϕ_(mk) ₁ +c_(0,k) ₀ −ϕ_(0k) ₀ from the set of estimatedphases.

At 1205, the present apparatus adds 2^(N−1) candidate codes to acandidate set S_(Φ) _(d) for direction Φ_(d).

At 1206, the present apparatus determines if k₀≥2^(Q)−1, where Q is anumber of bits in a phase shifter.

If at 1206 the present apparatus determines that k₀<2^(Q)−1, then thepresent method proceeds to 1207. If at 1206 the present apparatusdetermines that k₀≥2^(Q)−1, then the present method proceeds to 1208.

At 1207, the present apparatus updates the phase on the first antenna tok₀=k₀+1 and the method returns to 1204.

At 1208, the present apparatus selects a best candidate code that givesa maximum power in direction Φ_(d) from the candidate set S_(Φ) _(d) .

At 1209, the present apparatus determines if d≥L−1, where L is a totalnumber of steering directions.

If d<L−1, the present apparatus updates the steering direction to d=d +1at 1210 before returning to 1202. If d≥L−1, the present systemterminates the process.

It should be appreciated that various embodiments of the presentdisclosure and the terms used therein are not intended to limit thetechnological features set forth herein to particular embodiments andinclude various changes, equivalents, or replacements for acorresponding embodiment. With regard to the description of thedrawings, similar reference numerals may be used to refer to similar orrelated elements. It is to be understood that a singular form of a nouncorresponding to an item may include one or more of the things, unlessthe relevant context clearly indicates otherwise. As used herein, eachof such phrases as “A or B,” “at least one of A and B,” “at least one ofA or B,” “A, B, or C,” “at least one of A, B, and C,” and “at least oneof A, B, or C,” may include any one of, or all possible combinations ofthe items enumerated together in a corresponding one of the phrases. Asused herein, such terms as “1st” and “2nd,” or “first” and “second” maybe used to simply distinguish a corresponding component from another,but does not limit the components in other aspect (e.g., importance ororder). It is to be understood that if an element (e.g., a firstelement) is referred to, with or without the term “operatively” or“communicatively”, as “coupled with,” “coupled to,” “connected with,” or“connected to” another element (e.g., a second element), it means thatthe element may be coupled with the other element directly (e.g.,wiredly), wirelessly, or via a third element.

A method according to various embodiments of the disclosure may beincluded and provided in a computer program product. The computerprogram product may be traded as a product between a seller and a buyer.The computer program product may be distributed in the form of amachine-readable storage medium (e.g., compact disc read only memory(CD-ROM)), or be distributed (e.g., downloaded or uploaded) online viaan application store (e.g., Play Store™), or between two user devices(e.g., smart phones) directly. If distributed online, at least part ofthe computer program product may be temporarily generated or at leasttemporarily stored in the machine-readable storage medium, such asmemory of the manufacturer's server, a server of the application store,or a relay server.

According to various embodiments, each component (e.g., a module or aprogram) of the above-described components may include a single entityor multiple entities. One or more of the above-described components maybe omitted, or one or more other components may be added. Alternativelyor additionally, a plurality of components (e.g., modules or programs)may be integrated into a single component. In such a case, theintegrated component may still perform one or more functions of each ofthe plurality of components in the same or similar manner as they areperformed by a corresponding one of the plurality of components beforethe integration. Operations performed by the module, the program, oranother component may be carried out sequentially, in parallel,repeatedly, or heuristically, or one or more of the operations may beexecuted in a different order or omitted, or one or more otheroperations may be added.

Although certain embodiments of the present disclosure have beendescribed in the detailed description of the present disclosure, thepresent disclosure may be modified in various forms without departingfrom the scope of the present disclosure. Thus, the scope of the presentdisclosure shall not be determined merely based on the describedembodiments, but rather determined based on the accompanying claims andequivalents thereto.

1. A method comprising: (a) turning on an antenna of an antenna array,wherein other antennas of the antenna array are turned off; (b)measuring power for the antenna at each phase of a phase array; (c)repeating step (b) for each antenna of the antenna array; and (d)estimating gain errors based on the measured power for each antenna ofthe antenna array at each phase of the phase array.
 2. The method ofclaim 1, further comprising selecting a first reference phase for afirst antenna of the antenna array.
 3. The method of claim 2, furthercomprising selecting a second reference phase for a second antenna ofthe antenna array.
 4. The method of claim 3, wherein selecting thesecond reference phase comprises performing first power measurementswith the second antenna turned on for each phase of the phase array andwith the first antenna turned on at the first reference phase, whileother antennas of the antenna array are turned off.
 5. The method ofclaim 4, wherein the second reference phase is 90 degrees apart from thefirst reference phase.
 6. The method of claim 5, further comprisingperforming second power measurements, wherein the first antenna isturned on at the first reference phase, and each antenna of the antennaarray other than the first antenna and the second antenna issuccessively turned on one at a time at each phase of the phase arraywhile remaining antennas of the antenna array are turned off; performingthird power measurements, wherein the second antenna is turned on at thesecond reference phase, and each antenna of the antenna array other thanthe first antenna and the second antenna is successively turned on oneat a time at each phase of the phase array while remaining antennas ofthe antenna array are turned off; and estimating phases for each antennaof the antenna array other than the first antenna and the second antennabased on the second power measurements and the third power measurements.7. The method of claim 6, further comprising determining a thirdreference phase of a third antenna of the antenna array using values ofphase estimates made for the third antenna.
 8. The method of claim 7,wherein the third reference phase is 90 degrees apart from the secondreference phase.
 9. The method of claim 8, further comprising:performing fourth power measurements with the first antenna turned on ateach phase of the phase array other than the first reference phase andthe second antenna turned on at the second reference phase, while theother antennas of the antenna array are turned off; performing fifthpower measurements with the first antenna turned on at each phase of thephase array other than the first reference phase and the third antennaturned on at the third reference phase, while the other antennas of theantenna array are turned off; and estimating phases for the firstantenna based on the fourth power measurements and the fifth powermeasurements.
 10. The method of claim 7, further comprising determininga fourth reference phase of the third antenna using the values of phaseestimates made for the third antenna.
 11. The method of claim 10,wherein the fourth reference phase is 90 degrees apart from the firstreference phase.
 12. The method of claim 11, further comprising:performing sixth power measurements with the second antenna turned on ateach phase of the phase array other than the second reference phase andthe third antenna turned on at the fourth reference phase, while theother antennas of the antenna array are turned off; and estimatingphases for the second antenna based on the first power measurements andthe sixth power measurements.
 13. The method of claim 12, furthercomprising optimizing the estimated gain errors and phase errors foreach phase of the phase array for each antenna of the antenna array by aleast squared distance criteria between the first power measurements,the second power measurements, the third power measurements, the fourthpower measurements, the fifth power measurements, the sixth powermeasurements, and expected power measurements based on estimated gainerrors and estimated phase errors.
 14. The method of claim 13, whereinoptimizing the estimated gain errors and phase errors is based on adistance metric criteria between the first power measurements, thesecond power measurements, the third power measurements, the fourthpower measurements, the fifth power measurements, the sixth powermeasurements, and the expected power measurements.
 15. The method ofclaim 14, further comprising: generating codewords based on the updatedphases and gains for the antennas of the antenna array; and generating acodebook from the codewords.
 16. The method of claim 15, furthercomprising: selecting a direction; calculating powers of codewords inthe selected direction based on the estimated gain errors and phaseerrors of the antennas of the antenna array; and determining thecodeword in the codebook that generates a maximum power in the selecteddirection.
 17. An apparatus, comprising: a power meter; and a controllerconfigured to (a) turn on an antenna of the antenna array, wherein otherantennas of the antenna array are turned off; (b) control the powermeter to measure power for the antenna at each phase of a phase array;(c) repeat step (b) for each antenna of the antenna array; and (d)estimate gain errors based on the measured power for each antenna of theantenna array at each phase of the phase array.
 18. The apparatus ofclaim 17, wherein the controller is further configured to select a firstreference phase for a first antenna of the antenna array.
 19. Theapparatus of claim 18, wherein the controller is further configured toselect a second reference phase for a second antenna of the antennaarray.
 20. The apparatus of claim 19, wherein the controller is furtherconfigured to perform first power measurements with the second antennaturned on for each phase of the phase array and with the first antennaturned on at the first reference phase, while other antennas of theantenna array are turned off.